You add cards to your wallet on Apple Watch using the Watch app on your iPhone.
In the Watch app, scroll down and tap Wallet & Apple Pay and then tap Add Card to add a card to your Apple Watch.
See this article from Apple for more information...
https://support.apple.com/en-us/HT204506#applewatch
- Open the Apple Watch app on your iPhone, and go to the My Watch tab. If you have multiple watches, choose one.
- Tap Wallet & Apple Pay.
- Follow the steps to add a card.6 To add a new card, tap Add Card. If you're asked to add the card that you use with your Apple ID, cards on other devices, or cards that you’ve recently removed, choose them, then enter the card security codes. In China mainland, you might be required to create or update a 6-digit passcode.
- Tap Next. Your bank or card issuer will verify your information and decide if you can use your card with Apple Pay. If your bank or issuer needs more information to verify your card, they'll ask you for it. When you have the information, go back to Wallet & Apple Pay and tap your card.
- After your bank or issuer verifies your card, tap Next. Then start using Apple Pay.